Stabilizing framerate of Android games

I've been playing some fast-paced, focus-demanding games like Super Hexagon and Size DOES Matter on my Sony Xperia Z1 recently, and I've noticed something that has been bothering me.

Sometimes I get frame rate hiccups, stutters, drops, or whatever you want to name it, while playing these games. This happens most often on the train, on which I suspect it happens due to constant changes in connection types, such as Edge, 3G, 4G and possibly even Wi-Fi, which might then trigger stuff in background processes. (I don't know any of this for sure, it's just pure speculation).

Anyways, this is a really annoying problem, since a single badly timed stutter can ruin what could have been a perfect playthrough.

So here's my question: What can I do to eliminate, or at least minimize these stutters while playing?

Going into Airplane Mode seems to help alleviate the problem a bit, however, if I want to have my score posted in the leaderboards, e.g. in Size DOES Matter, I need to have an internet connection. What to do..? :-/